Question

Determine the whole number unknowns for the solution set of the given graph of an inequality in two variables.
__ x < __ y

Answer 1

what are the numbers then

Answer 2

To determine the whole number unknowns for the solution set of the inequality \( x < y \), we need to analyze what this inequality represents.

1. **Understanding the Inequality:**
- The inequality \( x < y \) means that the value of \( y \) must be greater than the value of \( x \).
- This can be considered in a coordinate system (with \( x \) and \( y \) as axes), where the region of interest is above the line \( y = x \).

2. **Finding Whole Number Solutions:**
- We need to find the pairs of whole numbers (non-negative integers) \( (x, y) \) that satisfy the inequality \( x < y \).
- For whole number solutions, \( x \) can take values from 0 upwards, and for each specific integer value of \( x \), \( y \) must be greater than \( x \).

3. **Example Solutions:**
- If \( x = 0 \), then \( y \) can be \( 1, 2, 3, \ldots \) (i.e., \( y \) can be any whole number greater than \( 0 \)).
- If \( x = 1 \), then \( y \) can be \( 2, 3, 4, \ldots \) (any whole number greater than \( 1 \)).
- If \( x = 2 \), then \( y \) can be \( 3, 4, 5, \ldots \) (i.e., any whole number greater than \( 2 \)).
- This pattern continues indefinitely for all whole numbers.

4. **Formulating the Solution Set:**
- The solution set can be written as pairs \( (x, y) \) such that:
- \( x \) is a whole number \( \geq 0 \)
- \( y \) is a whole number \( > x \)

Thus, the whole number unknowns for the solution set of the inequality \( x < y \) consist of infinite pairs of whole numbers \( (x, y) \), where for each whole number \( x \), \( y \) must always be greater than \( x \).

Answer 3

To list the specific pairs of whole numbers (non-negative integers) that satisfy the inequality \( x < y \), we can outline some of the possible combinations systematically.

Here’s a breakdown of the values for \( x \) and the corresponding values for \( y \):

1. **For \( x = 0 \)**:
- Possible values for \( y \): \( 1, 2, 3, 4, \ldots \)

2. **For \( x = 1 \)**:
- Possible values for \( y \): \( 2, 3, 4, 5, \ldots \)

3. **For \( x = 2 \)**:
- Possible values for \( y \): \( 3, 4, 5, 6, \ldots \)

4. **For \( x = 3 \)**:
- Possible values for \( y \): \( 4, 5, 6, 7, \ldots \)

5. **For \( x = 4 \)**:
- Possible values for \( y \): \( 5, 6, 7, 8, \ldots \)

6. **Continuing this pattern**:
- Generally, for any whole number \( x \), \( y \) will be any whole number greater than \( x \).

So, some example pairs of \( (x, y) \) that satisfy \( x < y \) include:

1. \( (0, 1) \)
2. \( (0, 2) \)
3. \( (0, 3) \)
4. \( (1, 2) \)
5. \( (1, 3) \)
6. \( (2, 3) \)
7. \( (2, 4) \)
8. \( (3, 4) \)
9. \( (3, 5) \)
10. \( (4, 5) \)

And so on...

### Summary of Numbers
The full solution set of whole number pairs \( (x, y) \) such that \( x < y \) can be expressed as:

- **For each non-negative integer \( x = 0, 1, 2, 3, \ldots \)**,
- **The corresponding \( y = 1, 2, 3, 4, \ldots (y > x) \)**.

In terms of numeric pairs:

\[
\{(0,1), (0,2), (0,3), (0,4), \ldots, (1,2), (1,3), (1,4), \ldots, (2,3), (2,4), \ldots\}
\]

The process gives us an infinite set of pairs where \( y \) is always greater than \( x \).